在空间形式中,构造了子流形的一类泛函, 其包含
r极小泛函与体积泛函(极小)作为特殊情形, 此类泛函的临界点称之为
-平行子流形. 对于
-平行子流形, 给出了代数,微分和变分刻画. 更进一步, 研究了
-平行子流形的稳定性, 证明了Simons型不存在定理: 在一定条件下
-函数
为正), 球面中不存在稳定的
-平行子流形.
Abstract
A class of functionals is found in space forms such that its critical points include
r-minimal submanifolds and minimal submanifolds as special cases. The critical points are defined as
-parallel submanifolds. We obtain algebraic, differential and variational characterizations of the
-parallel submanifolds. Moreover, we prove a Simons' type nonexistence theorem which says that in the unit sphere there exists no stable
-parallel submanifold with its corresponding
-function
positive.
关键词
(r+1,λ)-平行子流形 /
(r,λ)-函数 /
Qr 算子
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Key words
(r+1,λ)-parallel submanifold /
(r,λ)-function /
Qr operators
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参考文献
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脚注
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